Energy strikes a vertical hemispherical plate with an intensity of 640 W/m2. The absorptivity is thrice the transmissivity and twice the reflectivity. Determine the rate of transmissiona)236.74 W/m2b)116.37 W/m2c)187.87 W/m2d)456.09 W/m2Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given data:
Intensity of energy, I = 640 W/m²
Absorptivity, α = 3T and
Reflectivity, ρ = 2T

where T is the transmissivity.

To find: Rate of transmission.

Solution:
Total energy incident on the plate is given by the sum of transmitted, absorbed and reflected energy.
I = It + Ia + Ir

From the given data,
α = 3T and ρ = 2T
Hence, T = (1 - α - ρ) / 2
Putting the values, we get
T = (1-3T-2T)/2
T = 1/5

Now, using the law of conservation of energy, we have
It = I(1 - α - ρ)
Substituting the values of α and ρ, we get
It = I(1 - 3T - 2T)
It = 640(1 - 3/5 - 2/5)
It = 116.37 W/m²

Therefore, the rate of transmission is 116.37 W/m².

Hence, option (B) is the correct answer.

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